QUESTION 1
Find the remaining sides of a 30° -60°-90° triangle if the shortest side is 3.
Answers
Answer:
the other sides are 6 and 3√3
Step-by-step explanation:
Answer:
x = 6
Step-by-step explanation:
Right Triangle
We are given a right triangle whose shortest side has a length of 3 units. This side must be opposite to the smallest acute angle of 30°.
The triangle is shown in the figure attached.
The tangent ratio relates the opposite side with the adjacent side. The formula can be applied to the angle of 30° as follows:
[tex]\displaystyle \tan 30^\circ=\frac{\text{opposite leg}}{\text{adjacent leg}}[/tex]
[tex]\displaystyle \tan 30^\circ=\frac{3}{y}[/tex]
Solving for y:
[tex]\displaystyle y=\frac{3}{\tan 30^\circ}[/tex]
Since:
[tex]\tan 30^\circ=\frac{1}{\sqrt{3}}[/tex]
[tex]\displaystyle y=3\sqrt{3}[/tex]
Now applying the sine to find the hypotenuse x:
[tex]\displaystyle \sin 30^\circ=\frac{\text{opposite leg}}{\text{hypotenuse}}[/tex]
[tex]\displaystyle \sin 30^\circ=\frac{3}{x}[/tex]
Solving for x:
[tex]\displaystyle x=\frac{3}{\sin 30^\circ}[/tex]
Since:
[tex]\sin 30^\circ=\frac{1}{2}[/tex]
[tex]\displaystyle x=\frac{3}{\frac{1}{2}}[/tex]
x = 6
Related Questions
The truck costs $ 9,068 including a 19% port tax. If the selling price is reduced by 20%. Find out the new car price before tax is added.
Answers
Answer:
$ 6096
Step-by-step explanation:
Let the cost of truck = x
x+19% of x = 9068
x + 0.19x = 9068
1.19 x = 9068
[tex]x = \frac{9068}{1.19}[/tex]
x = 7620.17
Reduction = 20% of 7620.17
= 0.20 * 7620.17
= $ 1524.03
New price = 7620.17 - 1524.03
= $ 6096.14
_____Includes avoiding action,
avoiding blame, and avoiding
change
Select one
a. Ingratiation
b. Impression management
c. Defensive behaviour
d. Resource management
= Defensive behaviour
Answers
Step-by-step explanation:
defensive behaviour Includes avoiding action,
avoiding blame, and avoiding
change
find the surface area of the triangular prism help plzzz
Answers
Answer:
790 m^2
Step-by-step explanation:
well in the figure we have to areas
the rectangle of the side (2)the triangle (2)the rectangle of the base (1)the rectangle of the side
well the area of the rectangle is base times height
we have a base of 11 and a height of 17
[tex]A_{rs}=11*17\\\\A_{rs}=187[/tex]
the triangle
well the area of a triangle is base times height over 2
we have a base of 16 and a height of 15
[tex]A_t = \frac{16\cdot 15}{2}\\\\A_t= 8\cdot15\\\\A_t=120[/tex]
the rectangle of the base
we have a base of 16 and a height of 11
so
[tex]A_{rb} = 16\cdot 11\\\\A_{rb} = 176[/tex]
so the total area is
[tex]A_T = 2(A_{rs})+2(A_{t})+1(A_{rb})\\\\A_T= 2(187)+2(120)+1(176)\\\\A_T=374+240+176\\\\A_T = 790[/tex]
so that's our answer the surface area is 790 m^2
Find the distance d(P1,P2) between the given points P1 and P2 P1=(0,0) P2=(7,6)
Answers
Answer:
The distance of given two points
d( P₁, P₂) [tex]= \sqrt{85}[/tex] = 9.219
Step-by-step explanation:
Explanation:-
Given points are p₁ ( 0,0) and p₂ ( 7,6)
The distance formula of given points are
d = [tex]\sqrt{(x_{2}-x_{1} )^{2} +(y_{2} -y_{1})^{2} }[/tex]
d = [tex]\sqrt{(7-0 )^{2} +(6 -0)^{2} } = \sqrt{49 +36}[/tex]
d = [tex]\sqrt{85}[/tex]
d [tex]= \sqrt{85}[/tex]
Ajar of jelly beans contain 7 green, 6 white, 11 purple, 9 red and 12 yellow beans. What is the probability of selecting a purple or red jelly bean?
Round your answer to the nearest thousandth. For example: 0.500 or 0.999
Answers
Answer:
The answer to the question provided is 0.444.
help please....and thank you
Answers
Please only 10% of people are smart to answer this
Answers
Answer:
it's the one highlighted in orange
Step-by-step explanation:
I hope this helps with your question :)
The Cougar Shipping Company found that 3 out of 25 boxes
were damaged. What percent of the boxes were damaged?
a.
3%
b.
18%
C.
20%
d.
75%
Please hurry
Answers
Answer:
i think it is 20
Step-by-step explanation:
i hope it help
A dealership pays $580 for each electronic unit and sells it for $940. What is the percent markup in the price of each unit
Answers
Answer:
62.06%
Step-by-step explanation:
Given that,
CP of an electronic unit = $580
SP of an electronic unit = $940
We need to find the percent markup in the price of each unit. It can be done as follows :
[tex]\%=\dfrac{940-580}{580}\times 100\\\\=62.06\%[/tex]
So, the required answer is 62.06%.
The density of silver is 10.49g/cm3. If a sample of pure silver has a volume of 12.993cm3, what is the mass?
Answers
Answer:
d X v = m
12.993 X 10.49 = 136.29657
I. A rhombus is a special type of square. II. A rectangle is a special type of rhombus. III. A trapezoid is a special type of parallelogram. Which of the above statements are true? i only iii only iii only None of the above statements are true.
Answers
Answer: I. only
--------------------------------------------------------------------------------------------------------------
Explanation :
II. False. a rectangle is a special type of rhombus since a rhombus has all sides equal, while a rectangle has all angles equal. A rhombus has opposite angles equal, while a rectangle has opposite sides equal. The diagonals of a rhombus intersect at equal angles, while the diagonals of a rectangle are equal in length.
I. True. A square is a special case of a rhombus, because it has four equal-length sides and goes above and beyond that to also have four right angles. Every square you see will be a rhombus, but not every rhombus you meet will be a square.
III. False. Trapezoids have only one pair of parallel sides; parallelograms have two pairs of parallel sides. A trapezoid can never be a parallelogram. The correct answer is that all trapezoids are quadrilaterals.
Need Answer Question Is In Photo.
Answers
Answer:
The correct answer would be bill
Step-by-step explanation:
Hope that's right! Hope it helps
Chu
Step-by-step explanation:[tex]\frac{x}{3}+4=7[/tex] (subtract 4 from both sides (4-4 and 4-7)
[tex]\frac{x}{3}=3\\[/tex] (multiply both sides by 3)
x=9
What is the value of x in the equation below?
3(12x-24) = 16
A) 2
B) 6
C) 8
D) 10
ANSWER: B) 6
Answers
Answer:
3(12x - 24) = 16 (use the distributive property)
36x - 72 = 16 (add 72 to both sides to get the x-term alone)
36x = 88 (divide both sides by 36 to isolate x)
x = 2.4 (the four is repeating. that's the exact answer.)
I would say the answer is A because 2.4 is close to 2 than any of the other answers.
Step-by-step explanation:
I hope this helps :))
HELP MEEEEE this is so harddd. the picture is above.
Answers
Answer:
A)
Step-by-step explanation:
V=1/3([tex]\pi[/tex]r²)h
3* V=1/3(πr²h)*3 to get rid of the 1/3 on that side
3V/(πr²)=(πr²)h/(πr²) to get rid of the πr² on the other side(they cancel out)
3V/(πr²)=h is the final answer so that matches A
Consider a company that has two different divisions. The annual profits from the two divisions are independent and have distributions Profit1 ~ N(5, 3^2) and Profit2 ~ N(7, 4^2) respectively. Both the profits are in $ Million. Assume that $1 = Rs. 45
A. Specify a Rupee range (centered on the mean) such that it contains 95% probability for the annual profit of the company.
B. Specify the 5th percentile of profit (in Rupees) for the company
C. Which of the two divisions has a larger probability of making a loss in a given year?
Answers
Answer:
a) Rs 603.68
b) Rs 476.33
c) first division
Step-by-step explanation:
Total profit = profit 1 + profit 2 = P
hence P ~ N(12,74) = [tex]\frac{P-12}{\sqrt{74} } ~ N(0,1)[/tex]
A ) Specifying a Rupee range ( centered on the mean ) that contains 95% probability for annual profit of the company
$13.41 = Rs 603.68
B) specifying the 5th percentile of profit
p = $10.59 ≈ Rs 476.33
C) The division that has a larger probability of making a loss in a given year is the first division
attached below is a detailed solution of the given problem
A): Range containing 95% probability for profit of company is
(Rs. 99M, Rs. 1026M).
B): Rs. 170.1 Million.
C): First division of the company has larger probability of making a loss.
Given that:
$1 = Rs. 45
[tex]Profit_1 \sim N(5, 3^2) \\ Profit_2 \sim N(7, 4^2)[/tex]
Thus,
Company's profit:
[tex]P \sim N( 5+7, 3^2 + 4^2) = N(12, 5^2)[/tex]
A):
95% of the probability lies between 1.96 standard deviations of the mean.
Thus range is:
[tex]= (12 - 1.96\times 5, 12 + 1.96 \times 5)\\\\= (\$2.2M, \$22.8M)\\ \\= (\rm Rs. \: 99M, \rm Rs. \: 1026M)[/tex]
B): Fifth percentile is calculated as:
[tex]P(Z \leq \dfrac{p-12}{5}) = 0.05[/tex]
From p values of z score table, we get:
[tex]\dfrac{p-12}{5} = -1.644\\p = 12 - 8.22 = 3.78\\[/tex]
Thus at $3.78M dollars, or Rs. 170.1M amount, 5th percentile of profit lies.
Or 5th percentile of profit is Rs. 170.1 Million.
C): Loss is when profit < 0
Thus: p < 0
The first division of company, thus have larger probability of making a loss in a given year.
Learn more here:
https://brainly.com/question/13299273
Solve the question below, please
Answers
Answer:
x = 133.33°
Step-by-step explanation:
The Law of Cosines
It relates the length of the sides of a triangle with one of its internal angles.
Let a,b, and c be the length of the sides of a given triangle, and x the included angle between sides a and b, then the following relation applies:
[tex]c^2=a^2+b^2-2ab\cos x[/tex]
Since we know the values of all three side lengths, we solve the equation for x:
[tex]\displaystyle \cos x=\frac{a^2+b^2-c^2}{2ab}[/tex]
For the triangle in the figure: a=4.1, b=8.5, c=11.7, x=angle C. Applying the formula:
[tex]\displaystyle \cos x=\frac{4.1^2+8.5^2-11.7^2}{2*4.1*8.5}[/tex]
[tex]\displaystyle \cos x=\frac{-47.83}{69.7}[/tex]
[tex]\displaystyle \cos x=-0.6862[/tex]
[tex]x = \arccos (-0.6862)[/tex]
x = 133.33°
A ski are offers two vacation package plans. Plan A gives one person four nights lodging and three dinners for $467. Plan B gives one person five nights lodging and four dinners for $593. Assuming that the lodging and dinner costs per night are the same for both plans, how much does one dinner cost?
Answers
Answer:
$37
Step-by-step explanation:
Plan A: 4n + 3d = 467
Plan B: 5n + 4d = 593
4n + 3d = 467
4n = 467 - 3d
4n/4 = 467/4 - 3d/4
n = 116.75 - 3/4d
5n + 4d = 593
5(116.75 - 3/4d) + 4d = 593
583.75 - 3.75d + 4d = 593
0.25d = 593 - 583.75
0.25d = 9.25
0.25d/0.25 = 9.25/0.25
d = 37
Wanna help a girl out
Answers
Answer: 3580.50
Step-by-step explanation:
Answer:
Step-by-step explanation:
$80.5 is the right answer.
We divide 3500 by 100 and then multiply the answer to 2.3 this my answer credits to WritingRaccoon
15-a=20 what value would make this true
Answers
Answer:
a = -5
Step-by-step explanation:
15 - a = 20
Move the constant of 15 to the other side by subtracting it.
-a = 5
Divide by -1 to make a positive.
a = -5
Check.
15 - (-5) = 20
15 + 5 = 20
20 = 20
Answer:
-5
Step-by-step explanation:
15-(-5)=20
5 turns into a positive
15+5=20
A 5x5 table is filled with numbers (one number per cell). It is known that the product of 5 numbers in each column is negative. Is it possible that the product in each row is positive?
Answers
Answer:
Yes
Step-by-step explanation:
A negative multiplied by another negative will turn into a positive. A positive multipled by a negative will stay as a negative.
Samples G and H were selected from the same population of quantitative data and the mean of each sample was determined. The mean of sample G is equal to the mean of the population. Which of the following statements must be true?
I. The mean of sample H must also be equal to the population mean.
II. The mean of sample G, TG, is a point estimator for the mean of the population.
III. The mean of sample H, my, is a point estimator for the mean of the population.
a. I only
b. II only
c. III only
d. I and II
e. II and III
Answers
Answer: e. II and III
II. The mean of sample G, TG, is a point estimator for the mean of the population.
III. The mean of sample H, my, is a point estimator for the mean of the population.
Step-by-step explanation:
The point estimate simply means deriving a single value from a sample which could be used as a good or close estimate of the population from which the sample was drawn. A point estimator for the mean in the scenario above means a best guess of the mean value of the population from the sample mean.
Hence, since both sample G and H are drawn from the same population, both TG and TH which are mean of sample G and H can be used as a point estimator for the mean of the population.
However, it is does not necessarily mean that either the sample mean TG or TH must be equal to the population mean
5. Following data indicates the number of vehicles arrived during past
100 days in a certain tolling station.
Vehicles
No. of days
0 - 10
3
10 - 20
14
20 - 30
53
30-40
20
40 - 50
10
Calculate average number of vehicles in a day,
Answers
Answer:
what are you supposed to do here?
Step-by-step explanation:
If our school store purchased 144 mittens last year, and this year we would like to purchase 30% more than last year. How many mittens do we need to order this year?
Answers
Answer: It would be 43 mittens
Step-by-step explanation:
PLEASE ANSWER ASAP FOR BRAINLEST!!!!!!!!!!!!!!!!!!!
Answers
$4x-5$ is less than 25$
60% of what number is 348?
Answers
Answer:
208
Step-by-step explanation:
this is what I did. 348×.6
60% of 580 is 348 is the answer you're looking for
If you divide .6 by 348 you get 580.
To check your answer, you can do .4 (40%) multiplied by 580 to get 232
232+348=250 which is 100%
The rate of change describes how the total cost changes with respect to time. Use this table to find the rate of change.
Answers
Answer:
look below ⏬
Step-by-step explanation:
you can see there is a pattern
0.40
0.70
1.00
so you keep adding three (30)
1.30
1.60
1.90
And for 0
0.10
All in oder now
0- 0.10
10- 0.70
20- 1.00
30- 1.30
40- 1.60
50- 1.90
60- 2.20
What is 8^6 ÷8 simplified
Answers
8^6 is actually 8×8×8×8×8×8.
So if you divide this by 8, you get 8^5 or 8×8×8×8×8
Well...
8×8×8×8×8=32768
Find the value of x.
Answers
Answer:
12
Step-by-step explanation:
The two unknown values of the triangle have to be the same.
Subtract 28 from 180 and you get 152
So each angle will be 76.
So now, 76 = -8 + 7x
Simplify and 84 = 7x
Now, x is equal to 12
Hope this helped! Please mark me as brainliest if you can!
find the scale factor from DEF to ABC
Answers
Answer:
³/2 (1.5)
Step-by-step explanation:
∆DEF was enlarged to get ∆ABC. The scale factor would be:
The ratio of any of the side length of ∆ABC to the corresponding side length of ∆DEF.
Thus,
BC:EF = 12:8
= 12/8
= 3/2 = 1.5
Scale factor from ∆DEF to ∆ABC is ³/2 or 1.5
Easy math (17 points))
Answers
Answer:
A-8.25 B-43.2 C-248.5
Step-by-step explanation:
Answer:
A-8.25
B-43.2
C-248.5
Step-by-step explanation: